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We propose the optical zero-spin-to-orbital angular momentum and linear-to-vector polarization conversion realization by an optically active plate with a topological charge. By the geometric phase, the zero spin will also contribute to the orbital optical angular momentum and induce the optical spin-to-orbital angular momentum conversion. Moreover, the proposed angular momentum converter can convert the polarization from linear to radial or azimuthal with high efficiency. We believe that the proposed efficient converter will find potential applications in the study of quantum information conversion, generation and interaction of vector fields, phase and polarization singularities, etc.